I never travel in the summer months, find them too crowded BUT understand with children in tow often the only time to travel for many. I also prefer colder temps than blazing sun but that's because I live in LA where we don't have weather, just sun. Anyway, I'd opt for August and I'd fly into Shannon and out of Dublin. West coast of Ireland stuns and I feel its the best way to introduce first timers to Ireland's beauty. I would also include Northern Ireland on your trip. That way you can say you visited two different countries. Also an excellent learning experience regarding about The Troubles as well the tragedy of the Titanic. If there are Game of Thrones fans in your group you might enjoy a tour while in Belfast. I suspect where the filmed scenes for the new Star Wars in Ireland will also generate some viewing interest.
Start perusing Vrbo and Airbnb websites as well as the main Ireland Bed and Breakfast website for accommodations. http://www.bandbireland.com Best to rent and do day trips. Don't miss Dingle, Slea Head, Gap of Dunloe, Skelig Michael, The Burren, NewGrange, Giants Causeway, or Glendalough. BEAUTIFUL island, wonderful people, what's not to like?!! Enjoy.